SOLUTION: a farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 foot of fence?

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Question 616476: a farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 foot of fence? What should the dimensions of the garden be to get this area?
Answer by lwsshak3(11628) About Me  (Show Source):
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a farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 foot of fence? What should the dimensions of the garden be to get this area?
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let x=length of each of the two sides perpendicular to the side of the barn
60-2x=length of third side parallel to side of the barn
Area=x(60-2x)
=60x-2x^2
=-2x^2+60x
complete the square
=-2(x^2-30x+225)+450
=-2(x-15)^2+450
maximum area=450 sqft
dimensions of garden: 15 ft by 30 ft